Page 253 - A Practical Companion to Reservoir Stimulation

NOMENCLATURE

tD = Dimensionless time Symbols
tDk/ = Dimensionless fracture time a = Poroelastic constant (Ch. 2)
= Time to end of wellbore storage effects, hr, s a, = Gas specific gravity (to air)
t, ,, h
t, = Injection time, hr P = Permeability anisotropy ratio, JkH/k,

tP = Producing time, hr (Ch. 1) y = Euler’s constant (Ch. 1)
tP = Pumping time, hr y = Shear strain (Ch. 2)
trod = Time for pad injection, hr y = Surface energy, BTU/ft’, J/m2 (Ch. 3)
T = Absolute temperature, OR, OK y = Fracture shape factor (Ch. 8)
T,, = Standard temperature y = Specific gravity (Ch. 9)

U = Velocity, ftJs, cm/s y = Shearrate, s-’
U/ = Terminal settling velocity, ftls, m/s (Ch. 5) ye = Gas specific gravity (to air)
u, = Slurry velocity, ft/s, m/s = Fracture shape factors (Ch. 3)

VP = Proppant specific volume, dimensionless Ap = Pressure difference, psi
Vl = Total specific volume, dimensionless Apt = Excess fracture pressure, psi, bar (Ch. 8)
V = Volume, ft7, m3 At = Time difference, hr
V, = Total volume of fluid injected, bbl, gal, m’ & = Longitudinal strain
77 = Coefficient of internal friction (Ch. 2)
V,, = Leaked off volume during pumping, bbl, m’
77 = Fluid efficiency
VL, = Leaked off volume during shut-in, bbl, m3
8 = Angle
V, = Pore volume, ft7, m’
p = Viscosity, cp
V,, = Well volume, bbl, m’
pli = Apparent viscosity, cp
W = Fracture width, in., ft, m
p = Density, lb/ft3, g/cc
W = Average fracture width, in., ft, m
p~ = Diverter cake mass per unit sandface area,
wI, = Propped fracture width, ft, m lb/ft?, kg/m’
xj = Fracture length, ft, m p,, = Proppant density, lb/ft’, g/cc

xk, = Acid fracture length, ft, m P!,,~,~, = Proppant density, Ib/ft’, kg/m’
Y = Linear distance, ft, m CT = Stress, psi, bar
Z = Gas deviation factor, dimensionless CT‘ = Effective stress, psi, bar
Z,, = Gas deviation factor at standard conditions 0‘ = Critical load, psi, Nt
OH,,,^^,, = Maximum horizontal stress, psi, bar

c%,,~,,~ = Minimum horizontal stress, psi, bar
0, = Vertical stress, psi, bar
z = Shear stress, psi, bar
z,, = Wall shear stress, lb/ft’, ke,, bar
@ = Porosity, fraction
@,, = Proppant pack porosity, fraction

V